The north pole of a magnet is brought down along the axis of a horizontal circular coil (figure). As a result the flux through the coil changes from $0.4$ Weber to $0.9$ Weber in an interval of half of a second. Find the average emf induced during this period. Is the induced current clockwise or anticlockwise as you look into the coil from the side of the magnet?

 

The flux of magnetic field through a closed conducting loop of resistance $0.4 \mathrm{\Omega }$ changes with time according to the equation $\mathrm{\varphi }=0.20{\mathrm{t}}^2+0.40\mathrm{t}+0.60 \mathrm{V}‐\mathrm{s}$ where $t$ is time in seconds. Find

$\left(\mathrm{i}\right)$ The induced emf at$\mathrm{t} = 2\mathrm{s}.$

$\left(\mathrm{ii}\right)$ The average induced emf in $\mathrm{t} = 0 \mathrm{to} \mathrm{t} = 5 \mathrm{s}.$

$\left(\mathrm{iii}\right)$Charge passed through the loop in $\mathrm{t} = 0 \mathrm{to} \mathrm{t} = 5\mathrm{s}$

$\left(\mathrm{iv}\right)$ Average current in time interval $\mathrm{t} = 0 \mathrm{to} \mathrm{t} = 5 \mathrm{s}$

$\left(\mathrm{v}\right)$Heat produced in$\mathrm{t} = 0 \mathrm{to} \mathrm{t} = 5\mathrm{s}.$

$\left(\mathrm{a}\right)$ The magnetic field in a region varies as shown in figure. Calculate the average induced emf in a conducting loop of area ${10}^{–3} {\mathrm{m}}^2$ placed perpendicular to the field in each of the $10 \mathrm{ms}$ intervals shown.
$\left(\mathrm{b}\right)$ In which interval(s) is the emf not constant? Neglect the behaviour near the ends of $10 \mathrm{ms}$ intervals.

Figure illustrates plane figures made of thin conductors which are located in a uniform magnetic field directed away from a reader beyond the plane of the drawing. The magnetic induction starts diminishing. Find how the currents induced in these loops are directed.

A uniform magnetic field B exists in a cylindrical region of radius $1 \mathrm{cm}$ as shown in figure. A uniform wire of length $16 \mathrm{cm}$and resistance $4.0 \mathrm{\Omega }$ is bent into a square frame and is placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of$1 \mathrm{T} {\mathrm{s}}^{-1}$, find the current induced in the frame.